展开 ((x^2+1)(x+1))/x

解答

展开

\frac{( x ^{2} + 1 ) ( x + 1 )}{x}

x^{2} + x + 1 + \frac{1}{x}

求解步骤

\frac{( x ^{2} + 1 ) ( x + 1 )}{x}

乘开

(x^{2} + 1) (x + 1) : x^{3} + x^{2} + x + 1

= \frac{x ^{3} + x ^{2} + x + 1}{x}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{3} + x ^{2} + x + 1}{x} = \frac{x ^{3}}{x} + \frac{x ^{2}}{x} + \frac{x}{x} + \frac{1}{x}

= \frac{x ^{3}}{x} + \frac{x ^{2}}{x} + \frac{x}{x} + \frac{1}{x}

使用法则

\frac{a}{a} = 1

\frac{x}{x} = 1

= \frac{x ^{3}}{x} + \frac{x ^{2}}{x} + 1 + \frac{1}{x}

消掉

\frac{x ^{3}}{x} : x^{2}

= x^{2} + \frac{x ^{2}}{x} + 1 + \frac{1}{x}

消掉

\frac{x ^{2}}{x} : x

= x^{2} + x + 1 + \frac{1}{x}

e x p an d x (x - 3 + 1 (x - 3) = 12)

e x p an d \frac{2 ( 1 - 3 s )}{3 ( 2 s + 1 )}

e x p an d \frac{6 ( a + h ) - 1}{5 ( a + h ) + 2}

e x p an d (2 x^{2} + 3 x + 1)^{7}

e x p an d \frac{x ( x + 1 )}{2 x - 1}